Lead Screw Torque Calculator
Estimate the torque, collar drag, motor power, linear travel speed, and self-locking tendency for lead screws, Acme screws, trapezoidal screws, and ball screws.
Calculation Breakdown
| Screw type | Typical efficiency | Thread friction guide | Common use |
|---|---|---|---|
| Dry steel Acme screw | 15% to 25% | 0.20 to 0.30 | Vises, simple clamps, slow adjusters |
| Lubricated Acme screw | 25% to 45% | 0.10 to 0.18 | Jacks, lifts, shop fixtures |
| Bronze nut power screw | 30% to 55% | 0.08 to 0.16 | Machine slides and lift columns |
| Trapezoidal screw | 25% to 50% | 0.10 to 0.20 | Metric actuators and positioning axes |
| Ball screw | 85% to 95% | 0.03 to 0.06 | CNC axes, automation, fast travel |
| Formula | Expression | Inputs used | Output |
|---|---|---|---|
| Ideal raising torque | F x lead / (2 x pi) | Axial load and lead | Torque before losses |
| Efficiency torque | ideal torque / efficiency | Load, lead, efficiency | Practical thread torque |
| Square thread torque | F x dm / 2 x tan(lambda + phi) | Mean diameter and friction | Geometry check |
| Collar torque | F x mu collar x dc / 2 | Load, collar friction, collar diameter | Thrust face drag |
| Power | torque x RPM x 2 x pi / 60 | Torque and speed | Motor watts |
| Motion preset | Load range | Lead habit | Torque note |
|---|---|---|---|
| Fine adjustment stage | Light thrust | Very low lead | Low power, high positioning resolution |
| Router Z axis | Medium vertical load | Moderate lead | Check holding torque when unpowered |
| Machine lift screw | High vertical load | Low to moderate lead | Collar drag can dominate the motor size |
| Ball screw CNC axis | Low friction thrust | Fast lead | Often back-drivable, brake may be needed |
| Clamp or press screw | High axial force | Low lead | Torque is mostly force generation |
| Check item | Quick target | Why it matters | Action if marginal |
|---|---|---|---|
| Self-locking | Lead angle below friction angle | Load may not back-drive the screw | Add brake or lower lead |
| Collar share | Below 35% of total torque | High collar drag wastes motor torque | Use thrust bearing |
| Screw stress | Well below yield | Axial load compresses or stretches screw core | Increase root diameter |
| Column buckling | Separate vertical screw check | Long screws can buckle before threads fail | Support ends or resize screw |
| Critical speed | Separate long screw check | High RPM can whip slender screws | Reduce RPM or add supports |
A lead screw is a device that will perform the task of converting rotational motion to linear motion while a lead screw carry a load. The amount of torque that is required to move a lead screw is dependent upon a number of factors, including the weight of the loads that is pushing against the lead screw, the distance that the lead screw advance during one rotation, the friction that exists within the threads of the lead screw, and the friction that exists at the thrust face of the lead screw. If these factors are not correctly account for in the calculation of the torque that is required to move the lead screw, the motor will either stall or it will waste energy fighting against the drag that is created by the lead screw.
The next factor to consider is whether or not the lead screw should automatically be held in place by the lead screw alone or if a mechanical brake is to be added to the system. The lead screw will have a lead angle that will determine whether or not it will back drive under a load. Lead angles that are shallow will prevent the lead screw from back driving under a load, which is an essential component of devices like clamps or vertical lifts.
How to Size a Motor for a Lead Screw
Lead angles that are steep will allow the lead screw to move at a faster rate with less effort (less torque) being require to move the lead screw. However, steep lead angles may allow the load to push the lead screw backward when the motor is turned off. The designer can compare the lead angle of the lead screw to the friction angle of the lead screw to determine whether or not the lead screw will stay in place.
If the lead angle is lower than the friction angle, then the lead screw will remain in place. However, if the lead angle is higher than the friction angle, the load can push the lead screw backward. Based off this calculation, the designer can decide whether or not the motor need to be sized for continuous holding current or not.
Another factor to consider are thread friction and efficiency. These are two different concept. Thread friction is the resistance that occurs between the two thread flanks of a lead screw.
Efficiency is the amount of energy that is left over after thread friction, bending losses, nut clearance, and lubrication are taken into account. For instance, dry steel Acme threads that are unlubricated may have an efficiency of only 20%. If grease is added to those steel Acme threads, the efficiency may increase to 40%.
Ball screws have higher efficiency; ball screws may have an efficiency of 80% or 90%. The efficiency of the lead screw can have an impact upon the size of the motor that is required to operate the lead screw. For instance, if a ball screw requires a motor to deliver 2 Nm of torque, the sliding lead screw may require 6 or 7 Nm of torque to perform the same task.
Collar friction is a factor that occurs outside of the threads of the lead screw. Collar friction can consume a large amount of torque. For instance, a plain thrust washer under a heavy vertical load may consume 30 or 40% of the total torque that is delivered to the lead screw prior to the lead screw threads begin to turn.
If a thrust washer is replaced with a thrust bearing, the amount of torque that is consumed by the collar friction will decrease. Collar diameter and friction are two separate factor to consider for this very reason: because collar friction can consume a large portion of the torque that is available for the lead screw threads. If the amount of torque that is used by the collar is equal to or greater than one-third of the total amount of torque that is budgeted for the system, a better bearing should be used instead of simply increasing the size of the motor.
Lead and pitch are two different measurements of a lead screw that are often confused with one another. However, they are used for different purposes. Lead is the distance that the lead screw advances during one complete rotation of the lead screw.
Pitch is the distance between adjacent thread crests of a lead screw. For single-start lead screws, the lead and pitch are the same value. However, for two-start lead screws, the lead will be twice the pitch of the lead screw.
Therefore, if a two-start lead screw is used in the design of a device, the same motor speed will result in twice the linear travel of the lead screw. Additionally, because the lead screw has two starts, the lead screw will require a different amount of torque to rotate. The lead should be used in the torque calculation instead of the pitch; otherwise, the motor that is selected will either be underpowered or oversized for the application.
Once the torque for a system is calculated, the speed and power of the motor can be calculated, as well. The power of the motor is calculated as the product of the rotational speed and the torque that the motor must exert. Power is expressed in watts or horsepower.
However, just as heat is the limiting factor for motors, heat is also the limiting factor for lead screws. For lead screws with low efficiency, the lead screw will turn a large portion of the power of the motor into heat at the nut of the lead screw. Therefore, high-speed lead screws with low lead angles may overheat the bronze nut of the lead screw, even if the size of the motor is correctly selected.
A service factor for the motor can be used to provide a margin for error due to startup conditions, shock loads, or lead screw ways that is sticky. The service factor acts as a protective measure for the motor. Self-locking tendency and back-drive behavior are different from the amount of torque that is required to rotate the lead screw.
For instance, even if a lead screw only requires a small amount of torque to raise a load on the lead screw, the lead screw may still require a brake to hold that load in place. The opposite extreme is also true: high-efficiency ball screws may require a substantial amount of continuous current to provide enough force to overcome the force of gravity. Self-locking tendencies are evaluated by comparing the lead angle of the lead screw to the friction angle of the screw.
This comparison provides an indication of whether or not the lead screw will remain in place when the motor is turned off. This evaluation is merely an indicator. Factors like temperature, lubrication, and vibration may change how the lead screw behave when it is in operation.
Buckling of the lead screw, the critical speed of the screw, and the life of the screw’s bearings are all factor that are outside of the calculation of the torque that is required to turn the screw. For instance, long lead screws that are vertical in their design may buckle under the compressive forces of the load placed upon the screw before the threads of the lead screw begin to yield to that load. Additionally, lead screws that are slender in their construction may whip end-to-end at high rotational speeds even if the amount of torque is low.
Reference tables can provide information about the efficiencies and friction coefficient of lead screws of different types. An approach to calculating a lead screw that can save time and ensure accuracy in the calculations is to perform the calculation with the expected numbers for the system. Then, each variable can be altered one at a time.
For instance, if the lead of the screw is increased, the amount of torque that is required to turn the screw will drop and the rotational speed that is achieved will increase. If the amount of collar friction is increased, the amount of torque that is required of the motor will increase, regardless of the lead screw threads. If the efficiency of the lead screw is decreased from 35% to 25%, the amount of torque required of the motor will increase 40%.
Most mistakes are made when a designer treats each variable as a fixed number. Yet, many variables of a lead screw system can be adjusted. For instance, the designer can alter the lead by changing the type thread of the screw.
The friction between the threads can be reduced by adding lubrication. The designer can reduce the amount of collar friction by using a thrust bearing instead of a thrust washer. By recognizing these variables as adjustable, the designer can better determine the size of the motor that will be required for the system.
